Vectors and scalarsp. 160

Physical quantities are any quantities we can measure, for example time, mass, weight, force, charge, etc.

We divide physical quantities into vectors and scalars.

A vector isa physical quantity with magnitude and direction.

A scalar isa physical quantity with magnitude only.

Vectors Scalars

FORCE

VELOCITY

TIME

MASS

ACCELERATION

CHARGE

՜𝐹

represents the force vector,

where F represents the magnitude of the force vector.

The length of the arrow represents the magnitude and the arrow head indicates the direction of the vector.

15 N; East

Equality of vectors

՜𝐹1= 15 N; East

՜𝐹2= 15 N; East

՜𝐹1=՜

𝐹2

Negative vectors

՜𝐹1= 15 N; East

՜𝐹2= -15 N = 15 N; West

Choose East as positive

Addition of vectors

՜𝐹1= 6 N; East

՜𝐹2= 8 N; East

Choose East as positive

Addition of vectors

՜𝐹1+՜

𝐹2= 6N + 8N = 14 N; East

Choose East as positive

՜𝐹1

՜𝐹2

Subtraction of vectors

՜𝐹1= 6 N; East

՜𝐹2= 4 N; West

Choose East as positive

Subtraction of vectors

՜𝐹1+՜

𝐹2= 6N + (-4N) = 2 N; East

Choose East as positive

՜𝐹1

՜𝐹2

A resultant is the single vector that has the same effect as two or more vectors together.

՜𝐹1

՜𝐹2

՜𝑅

Head-to-tail method to determine a resultant:

՜𝐹1

՜𝐹2

՜𝑅

՜𝐹3

Or: ՜𝑅

= 6 + (-4) + 6 = 8 N; East

Equilibrant of forces

The equilibrant is the single force resulting in equilibrium.

It balances the resultant of the other forces.

Its magnitude is equal to that of the resultant,

but its direction is directly opposite.

Homework

p. 166nos. 5, 7, 8.6, 8.7, 9.1, 9.2, 10.1, 10.2

5. A force F = 20 N acts to the right. Make a scale drawing with completelabels, of the 20 N force, using the scale 10 mm = 2 N.

՜𝐹

= 20 N; right

7. ՜𝐹

= 6 N to the right. Draw the following vectors according to scale and

provide labels:7.1 2 ՜

𝐹

2՜𝐹

Scale: 10mm = 1N

7. ՜𝐹

= 6 N to the right. Draw the following vectors according to scale and

provide labels:7.2 0,5 ՜

𝐹

0,5՜𝐹

Scale: 10mm = 1N

7. ՜𝐹

= 6 N to the right. Draw the following vectors according to scale and

provide labels:7.3

−𝐹

−𝐹

Scale: 10mm = 1N

7. ՜𝐹

= 6 N to the right. Draw the following vectors according to scale and

provide labels:7.4 -2 ՜

𝐹

-2՜𝐹

Scale: 10mm = 1N

8. Alice and Chris exert forces ՜𝐹1

and ՜𝐹2

respectively on a rope.

՜𝐹1

= 60 N eastwards and ՜𝐹2

= 150 N westwards.

8.6 Draw a head-to tail vector diagram to determine the resultant force ofthese two forces.

՜𝐹1

Scale: 10mm = 10N

՜𝐹2

՜𝑅

՜𝑅

= 90 N; westwards

8. Alice and Chris exert forces ՜𝐹1

and ՜𝐹2

respectively on a rope.

՜𝐹1

= 60 N eastwards and ՜𝐹2

= 150 N westwards.

8.7 Calculate the resultant force.

Choose east as positive:՜𝑅

= 60N + (-150N)

= -90 N= 90 N; westwards

9. A child exerts a force of 20 N on a wagon. The wagon experiences a frictional force of 8 N.

9.1 Draw a head-to-tail vector diagram to determine the resultant forceexerted on the wagon. Use an appropriate scale.

՜𝐹1

Scale: 10mm = 2N

՜𝐹2

՜𝑅

՜𝑅

= 12 N; forward

9. A child exerts a force of 20 N on a wagon. The wagon experiences a frictional force of 8 N.

9.2 Calculate the resultant force exerted on the wagon.

Choose east as positive:՜𝑅

= 20N + (-8N)

= 12 N= 12 N; forward

10. Peter exerts a force ՜𝐹1

= 400 N to the right on a motorcar. The

motorcar experiences a frictional force ՜𝐹2

to the left. The resultant

force of these forces is 280 N to the right.10.1 Use an appropriate scale to determine the frictional force ՜

𝐹2exerted

on the motorcar.

՜𝐹1

Scale: 10mm = 20N

՜𝑅 ՜

𝐹2

՜𝐹2

= 120 N; to the left

10. Peter exerts a force ՜𝐹1

= 400 N to the right on a motorcar. The

motorcar experiences a frictional force ՜𝐹2

to the left. The resultant

force of these forces is 280 N to the right.10.2 Calculate the frictional force ՜

𝐹2exerted on the motorcar.

Choose right as positive:280 = 400N + ՜

𝐹2

՜𝐹2

= -120 N

= 120 N; to the left